=(3x-5y)(5x-3y)

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Solution for =(3x-5y)(5x-3y) equation: 


Simplifying
0 = (3x + -5y)(5x + -3y)

Multiply (3x + -5y) * (5x + -3y)
0 = (3x * (5x + -3y) + -5y * (5x + -3y))
0 = ((5x * 3x + -3y * 3x) + -5y * (5x + -3y))

Reorder the terms:
0 = ((-9xy + 15x2) + -5y * (5x + -3y))
0 = ((-9xy + 15x2) + -5y * (5x + -3y))
0 = (-9xy + 15x2 + (5x * -5y + -3y * -5y))
0 = (-9xy + 15x2 + (-25xy + 15y2))

Reorder the terms:
0 = (-9xy + -25xy + 15x2 + 15y2)

Combine like terms: -9xy + -25xy = -34xy
0 = (-34xy + 15x2 + 15y2)

Solving
0 = -34xy + 15x2 + 15y2

Solving for variable 'x'.
Remove the zero:
34xy + -15x2 + -15y2 = -34xy + 15x2 + 15y2 + 34xy + -15x2 + -15y2

Reorder the terms:
34xy + -15x2 + -15y2 = -34xy + 34xy + 15x2 + -15x2 + 15y2 + -15y2

Combine like terms: -34xy + 34xy = 0
34xy + -15x2 + -15y2 = 0 + 15x2 + -15x2 + 15y2 + -15y2
34xy + -15x2 + -15y2 = 15x2 + -15x2 + 15y2 + -15y2

Combine like terms: 15x2 + -15x2 = 0
34xy + -15x2 + -15y2 = 0 + 15y2 + -15y2
34xy + -15x2 + -15y2 = 15y2 + -15y2

Combine like terms: 15y2 + -15y2 = 0
34xy + -15x2 + -15y2 = 0

Factor a trinomial.
(-5x + 3y)(3x + -5y) = 0


Subproblem 1
Set the factor '(-5x + 3y)' equal to zero and attempt to solve:

Simplifying
-5x + 3y = 0

Solving
-5x + 3y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3y' to each side of the equation.
-5x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
-5x + 0 = 0 + -3y
-5x = 0 + -3y
Remove the zero:
-5x = -3y

Divide each side by '-5'.
x = 0.6y

Simplifying
x = 0.6y

Subproblem 2
Set the factor '(3x + -5y)' equal to zero and attempt to solve:

Simplifying
3x + -5y = 0

Solving
3x + -5y = 0

Move all terms containing x to the left, all other terms to the right.

Add '5y' to each side of the equation.
3x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
3x + 0 = 0 + 5y
3x = 0 + 5y
Remove the zero:
3x = 5y

Divide each side by '3'.
x = 1.666666667y

Simplifying
x = 1.666666667y
Solution
x = {0.6y, 1.666666667y}

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